Nuclear ground state spins of the odd-mass strontium isotopesbetween A = 79 and 97 were determined by measurements of the hyperfine structure in the ionic transition 5s 2SI/2 -5p 2P3/9-The spins of 93Sr and 97Sr'are revised To I = 5/2 and I = I/2, respectively, while assignments for the remaining isotopes are confirmed.The sequence of strontium isotopes ranges from the N : 50 shell closure for 88Sr into the regions of well-developed deformation for both neutron-deficient and neutron-rich isotopes. Laser spectroscopy measurements of the ground state moments and radii mainly cover the transitional region of the neutron-deficient branch [1,2]. We have recently started a more extended investigation of the nuclear ground state properties in strontium in an on-line experiment at the mass separator ISOLDE at CERN. In this communication we report the determination of the spins for the odd-A isotopes with 79 S A S 97 from the atomic hyperfine structure (hfs). This series of sDins includes two controversial cases, 93Sr and 97Sr, where first spin assignments from nuclear spectroscopy were revised later on [3 7]. Among these, 97Sr deserves special attention since the odd-mass isotones with N = 59 are considered to be an excellent testing ground for nuclear models because of their unique situation in the narrow range of neutron numbers where shape coexistence is indicated [7,8].Our hfs measurements have been performed 5s 2SI/2 -5p 2F3/2 transition in the (l = 407.8 nm) of the Sr § ion. We used the technique of cellinear fast-beam laser spectroscopy and the experimental procedure is similar to that one described in ref. [9]. * Present ad'dress: Fhysikalisch-Technisc~e Bundesanstalt,